Y=(x+4)(x+19)

Solution for Y=(x+4)(x+19) equation:

=(Y+4)(Y+19)

We move all terms to the left:

-((Y+4)(Y+19))=0

We multiply parentheses ..

-((+Y^2+19Y+4Y+76))=0


We calculate terms in parentheses: -((+Y^2+19Y+4Y+76)), so:

(+Y^2+19Y+4Y+76)

We get rid of parentheses

Y^2+19Y+4Y+76

We add all the numbers together, and all the variables

Y^2+23Y+76

Back to the equation:

-(Y^2+23Y+76)


We get rid of parentheses

-Y^2-23Y-76=0

We add all the numbers together, and all the variables

-1Y^2-23Y-76=0

a = -1; b = -23; c = -76;
Δ = b2-4ac
Δ = -232-4·(-1)·(-76)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-15}{2*-1}=\frac{8}{-2}
=-4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+15}{2*-1}=\frac{38}{-2}
=-19
$